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Abstract

By slightly vibrating the mirrors in an interferometer at different frequencies, the photons’ trajectory information is stored in the light beam. To read out this information, we record the centroid location of the intensity distribution of output beam and Fourier analyze its time evolution. It is shown that every vibrating mirror contributes a peak in the Fourier spectrum. In other words, we can reveal the trajectory of the photons by figuring out the vibrating mirrors which ever interact with the light beam based on the Fourier spectrum. This techniques is not limited by the vibration amplitude of the mirrors.

Fourier spectrum of the output beam based on the intensity difference (3). (a) In the case of constructive interference, two peaks fA and fB appear in the Fourier spectrum as the signature of the two vibrating mirrors A and B in the interferometer; (b) In the case of destructive interference, some “noisy” peaks appear in the Fourier spectrum, besides the two peaks fA and fB.

Fourier spectrum of the output beam based on CLSID. The peaks in the Fourier spectrum have a one-to-one correspondence with the vibrating mirrors, no matter which type of interference, constructive or destructive, is set for the output beam.

A modified Mach-Zehnder interferometer. A small Mach-Zehnder interferometer is nested in the upper arm of the larger one, and a destructive interference is set for the beam F initially. Five mirrors slightly vibrate in the experiment at the frequency fA = 282Hz, fB = 296Hz, fC = 309Hz, fE = 318Hz and fF = 337Hz, respectively.

Fourier spectrum of the output beam in the experiment with nested interferometer based on CLSID. Every mirror in the interferometer contributes a peak in the Fourier spectrum, see the five red peaks, denoted as fA, fB, fC, fE and fF. In addition, many “noisy” peaks appear in the spectrum as a result of the combined contribution of two or more vibrating mirrors, see the lower blue peaks, e.g. f1 and f2.